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Talk:Team Viewer/@comment-201.50.116.232-20150119190616/@comment-3408861-20150821033400
I like Serena, your reason for giving HP a power of 1, is that doubling it means a fight can last twice as long. But this is only true against a given opponent. If your team BARELY beats a given dungeon, and then you go to a dungeon that is dealing damage twice as fast, and you were surviving by a combination of HP and REC, you need to double BOTH HP AND REC, to survive. (Correct me if I am wrong. Of course, you might do some different combination of increase, but the easiest one to analyze is to increase both equally.) In the most important, difficult battles, which last long after you've exhausted AP, your survival time approaches REC^1 as the number of battle turns increases -- you have to have almost enough REC to "tread water", so that your peak HP is dropping slowly. If your team is dying and you need to make some improvement, you will gain more by a percentage increase in REC, than by the same percentage increase in HP. If boss damage to you per turn averages B1, and you estimate how many hearts you get on average per turn, you can determine the "tread water" REC of R1, at which R1 * hearts = B1, Then starting with your H and R, Each turn you lose health (B1 - R * hearts) = (R1 * hearts - R * hearts) = (R1 - R) * hearts. You will survive (ignoring variability) for H / ( (R1 - R) * hearts) turns (during which you need to kill the boss). Suppose you were starting with R = 0.5 R1. A 50% improvement, to R = 1.5 x 0.5 R1 = 0.75 R1, would let you survive twice as many turns -- 1/(1 - 0.75) vs. 1/(1 - 0.5) is 4 vs 2. Whereas a 50% improvement in H merely lets you survive 50% longer; 1.5x as many turns. Trying to put into math that the most difficult battles gain more from the factor by which you increase REC than the factor by which you increase HP. If you double HP AND you double REC, (I believe) you can survive a case that is dealing twice the damage to you per turn. Therefore, the powers of HP and REC should sum to 1 (so that doubling both results in double the value). The only question is how much of that "1" should go to HP, and how much should go to REC. My experience tells me that at the high end, our teams are being limited by REC more than HP. So in searching for the "best" heroes, we should be giving more weight to REC than to HP. Do you encounter situations for which this is not true, and HP is more of an issue? In summary, if I am correct that doubling both HP and REC together should double a hero or team's survival value, then "correct" formulas will be of the form "A * H^(1-k) * R^k", and the only question is "what is the optimal 'k', for the typical teams we are building"? On the Effectiveness Table page, I propose k=2/3, resulting in formula "A * H^(1/3) * R^(2/3)".